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Tuesday, January 16, 2018

Heuristics For The Masses

You’ve seen me exercised over the misuse of words. You’ve seen me exercised over the arrogation of unearned authority; there’s certainly enough of that going around. You’ve surely seen me exercised over unfounded assertions of expertise. But today, I’m going to mount my high horse over the mistreatment of an important concept.

I’ve grown tired of seeing it misstated, especially as the misstatement undercuts the most important of all human mental processes: the one that makes learning possible.

“Entities ought not to be multiplied beyond necessity.” – William of Occam

The above quote is generally known as Occam’s Razor. (It’s also been called the principle of parsimony.) Few are the statements that have been misinterpreted more often than that one. The most common misinterpretation is that if a given phenomenon can be explained in a number of ways, the simplest explanation is most likely to be the correct one.

WRONG!

The laws of the universe do not favor simplicity over complexity. (Trust a specialist in general relativity to know that.) Nor is there any reason why they “should.” What, then, does Occam’s Razor “do for us?”

The answer is both more complex and more revealing than one might suppose. However, what it reveals isn’t some aspect of natural law, but rather the process by which we investigate causes and acquire knowledge.

The conceptual envelope in which Occam’s Razor belongs is called heuristics.

Herewith, a statement nonscientists will regard as rather shocking:

It is impossible to determine the cause of any natural phenomenon with absolute confidence.

As natural is one of the worst-abused words in the English language, allow me to clarify what I mean by it in the above. For the purposes of the coming diatribe, a “natural phenomenon” is distinguished from all other such phenomena in that no sentient agency deliberately brought it about. For the unbalanced pile of dirty dishes on the kitchen counter to fall and shatter is a natural phenomenon; for Mom to sweep up the shards, muttering about the laziness of the ingrates she keeps house for, is not.

Under this application of the word, natural phenomena are the consequences of the operation of natural laws, independent of human action or opinion. We probe those laws by the use of the scientific method:

Collect data about the phenomenon and the surrounding context.

Propose an “explanation:” i.e., a hypothesis about the cause.

Use the hypothesis to make a prediction that can be tested in a controlled experiment.

Perform the experiment and observe the results.

Did the result conform to the prediction?

If so, make further predictions premised upon the hypothesis and return to step 4.

If not, return to step 1.

Examine the above procedure very carefully. Note that if the scientist’s predictions are all confirmed by a properly controlled experiment, the hypothesis could be tested indefinitely. Only if an adequate experiment should fail to fulfill the associated prediction will the hypothesis be rejected.

An infinite number of successful predictions does not “prove” the “truth” of a hypothesis; it merely increases our confidence that “we’re on to something.” One failure of prediction blasts the hypothesis to pieces. This is the way scientists work, ever since Francis Bacon.

Keep this segment in mind as you proceed.

Occam’s Razor, while it doesn’t tell us anything about which of a group of alternate hypotheses is “correct,” does tell us something extremely valuable. In short, it establishes the order in which those hypotheses should be tested: simplest first.

This isn’t because “the simplest explanation is probably the right one;” it’s because the simpler the explanation, the easier it is to test! A simple explanation involves fewer causal elements than a complex one; therefore, designing an experiment to test the simple hypothesis is easier, and more likely to produce unambiguous results. Doing the investigation in that order improves the probability of quickly getting demonstrably wrong hypotheses out of our way.

Now, testability is critical. There are always untestable explanations for an event. This is particularly important in the case of irreproducible events. But scientists don’t concern themselves with things that happen only once. If it can’t be reproduced, we’ve got no shot at determining why it happened.

This leads us to the underlayer to Occam’s Razor: what William of Occam had in mind when he propounded it.

If you’ve been wondering why I’m so confident about the large-font assertion from earlier:

It is impossible to determine the cause of any natural phenomenon with absolute confidence.

...it’s because I can always propose an explanation that cannot be tested:

The phenomenon was not “natural,” but was brought about by the deliberate action of a conscious and purposeful actor.

The short form of the above explanation is “God did it.” And indeed, William of Occam was deeply concerned about that approach to the world. He was a Franciscan friar and theologian, a devout Christian man. He believed in God and His ultimate authority, but he disliked flip appeals to divine agency as explanations for the behavior of the natural world. Though he preceded Francis Bacon and the formulation of the scientific method by centuries, he had a sense for the importance of “keeping it simple.” To say of an event that “God did it” is to claim a gnosis. That assertion is unfriendly to the assumption that the laws of nature are knowable by investigation – and without that assumption, human knowledge cannot advance.

To sum up, Occam’s Razor is not a “law about natural law,” but a heuristic tool: a device that assists us in learning about the natural order. It doesn’t “privilege” simpler hypotheses over more complex ones; it merely sorts them into a preferred order for testing. While that order might mean that the investigator will hit upon the “correct” explanation later rather than sooner, it puts the odds in his favor.

But don’t imagine that simplicity is some organizing principle of natural law. All it takes is a semester of quantum physics to blast that notion to smithereens. Erwin Schrodinger would surely tell you so, but unfortunately, he’s dead.

3 comments:

I guess we need to know if anyone has observed Schrodinger in his coffin to know for sure! Thank you for this piece on William of Occam. It has always bugged me that most people get this SO very wrong, ad nauseum.